Chapter 12, Problem 1RQ

To determine

To evaluate: The intersection of best-response functions between firms.

Answer to Problem 1RQ

The intersection between firm’s responses proves to be graphical representation of Nash equilibrium.

Explanation of Solution

The following diagram shows the best-response functions of Firm-A and Firm-B.

  

From the above diagram, it is clear that Firm A’s best-response function depicts the profit- maximizing quantity by the quantity chosen by Firm ‘B’. Similarly, the Firm ‘B’ best-response function depicts the profit-maximizing quantity chosen by Firm ’A’. To get the Nash equilibrium, both firms have to contribute their best-responses. The point of intersection of both the responses Q’A’ and Q’B’ is at 40.

The diagram given in 12.2 depicts the intersection between the firm’s best response stating the Cournot model and similarly the diagram given in 12.3 depicts the intersection between the firm’s best response stating the Bertrand model of Nash equilibrium. This is because the intersection depicts the situation where both the firms are stable. There won’t be any incentives if any changes occur in the quantity in case of Cournot model and no incentives are entertained if there is change in prices in case of Bertrand model.

In case of any deviation from the intersection point, it will lead to responses related to the other firm. This situation can be settled only if the intersection point is reached again.

Economics Concept Introduction

Introduction:

Nash equilibrium: It is a situation where a stable state is created. At this stage, different participants interact with other and does not involve any gain or profit by change in strategy by one participant while other participants strategies remain constant.